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Simplifying 20s2 + -23sr + 6r2 = 0 Reorder the terms: -23rs + 6r2 + 20s2 = 0 Solving -23rs + 6r2 + 20s2 = 0 Solving for variable 'r'. Factor a trinomial. (2r + -5s)(3r + -4s) = 0Subproblem 1
Set the factor '(2r + -5s)' equal to zero and attempt to solve: Simplifying 2r + -5s = 0 Solving 2r + -5s = 0 Move all terms containing r to the left, all other terms to the right. Add '5s' to each side of the equation. 2r + -5s + 5s = 0 + 5s Combine like terms: -5s + 5s = 0 2r + 0 = 0 + 5s 2r = 0 + 5s Remove the zero: 2r = 5s Divide each side by '2'. r = 2.5s Simplifying r = 2.5sSubproblem 2
Set the factor '(3r + -4s)' equal to zero and attempt to solve: Simplifying 3r + -4s = 0 Solving 3r + -4s = 0 Move all terms containing r to the left, all other terms to the right. Add '4s' to each side of the equation. 3r + -4s + 4s = 0 + 4s Combine like terms: -4s + 4s = 0 3r + 0 = 0 + 4s 3r = 0 + 4s Remove the zero: 3r = 4s Divide each side by '3'. r = 1.333333333s Simplifying r = 1.333333333sSolution
r = {2.5s, 1.333333333s}
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